Surfaces roughness exponent

Fig. 3.19. Molecular dynamic simulation results for the fracture propagation in amorphous structures (with Lennard-Jones potential) show that the average fracture velocity crosses over to a higher value (ufinai from Uinitiaij indicated by the dotted lines) at the late stages of growth, as the crack size exceeds the typical size (correlation length) of the voids in the network. The inset shows that a corresponding crossover in the fractured surface roughness exponent also occurs along with the crossover in the fracture velocity (from Nakano et al 1995).

Therefore we can conclude that the surface roughness does not affect the scaling exponent (P) value without bothering whether we are considering the rough surfaces with same surface density or with different surfaee density. 

The slopes of the boiling curves in Fig. 30 increase with increasing roughness. For the smooth metal the approximate relation is h = C(AT)li. For the roughest surface the exponent is 24. In no case did these experi-... 

A. Hansen, J. Origin of the universal roughness exponent of brittle fracture surfaces stress-weighted percolation in the damage zone. Phys. Rev. Lett. 90, 045504 (2003)... 

Here, kgj is in (kmol/m2/s), Ps is the ambient pressure in (Pa), T is the liquid pool surface temperature (K), w is a 10 meter wind speed in (m/s), and n is an exponent that depends on atmospheric stability and surface roughness. Typical values for n range between 0.25 and 1. When n is equal to 0.25, the wind speed profile implied by the correlation is a 1/7 power law profile. For n = 0.25, equation (3-5) reduces to... 

Fig. 3.6. A typical computer-generated crack surface, with the roughness exponent ( = 0.85 (from Roux 1994).

At t — 0, w(L, 0) oc fi where the superscript (3 is the roughness growth kinetics exponent along the x direction. After a certain time, a steady-state contour is reached, w(L, oo) oc L , or in other words, a scale invariant fractal is obtained (self-affined fractal). The exponent a is the surface roughness (only when it is measured at scale lengths shorter than the interface). 

---